Chaos: Making a New Science

by James Gleick

In the Malthusian scenario of unrestrained growth, the linear growth function rises forever upward. For a more realistic scenario, an ecologist needs an equation with some extra term that restrains growth when the population becomes large. The most natural function to choose would rise steeply when the population is small, reduce growth to near zero at intermediate values, and crash downward when the population is very large. By repeating the process, an ecologist can watch a population settle into its long-term behavior—presumably reaching some steady state. A successful foray into mathematics for an ecologist would let him say something like this: Here’s an equation; here’s a variable representing reproductive rate; here’s a variable representing the natural death rate; here’s a variable representing the additional death rate from starvation or predation; and look—the population will rise at this speed until it reaches that level of equilibrium.